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We describe a mu-calculus which amounts to modal logic plus a minimization operator, and show that its satisfiability problem is decidable in exponential time. This result subsumes corresponding results for propositional dynamic logic with test and converse, thus supplying a better setting for those results. It also encompasses similar results for a logic of flowgraphs. This work provides an intimate...
A general paradigm for relating measures of succinctness of representation and complexity theory is presented. The measures are based on the new Private and Blindfold Alternation machines. These measures are used to indicate the inherent information (or "randomness") of a string, but with respect to time and space complexity classes. These measures are then used to show that the existence...
We introduce a new complexity measure, QR[f(n)], which clocks the size of formulas from predicate calculus needed to express a given property. Techniques from logic are used to prove sharp lower bounds in the measure. These results demonstrate space requirements for computations and may provide techniques for seperating Time and Space complexity classes because we show that: NSPACE[f(n)] ⊆ QR[(f(n))2/log(n)]...
Two complementary but equivalent semantic interpretations of a high level probabilistic programming language are given. One of these interprets programs as partial measurable functions on a measurable space. The other interprets programs as continuous linear operators on a Banach space of measures. It is shown how the ordered domains of Scott and others are embedded naturally into these spaces. Two...
We show the existence of polynomials with 0-1 coefficients that are hard to evaluate even when arbitrary preconditioning is allowed. Further we show that there are power series with 0-1 coefficients such that their initial segments are hard to evaluate.
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